Lew told reporters aboard Air Force One that the government would reach its borrowing authority on Feb. 7, and so-called "extraordinary measures" that allow the government to continue paying its bills would be exhausted before the end of next month.

"They need to act in that window,” Lew said of lawmakers, adding that he thought, "they've accepted that deadline."

House Republicans have expressed surprise at the tight timeframe, and some are questioning Lew's deadline.

Earlier this month, Senate Majority Leader Harry Reid (D-Nev.) suggested lawmakers had more time to resolve the debt-ceiling fight.

"That is not urgent. We keep getting different numbers on that. We think sometime in May that will be necessary," Reid said. "Maybe it's April. But we'll deal with it."

Reid's office later said the top Democrat wanted to deal with the debt ceiling “as soon as possible.”

Senate Minority Leader Mitch McConnell (R-Ky.) suggested earlier this month that the GOP wanted to "attach something significant for the country" — like the approval of the Keystone XL pipeline — to a debt-limit increase.

“Any president's request to raise the debt ceiling, whether this one or previous presidents, is a good opportunity to try to do something about the debt. I think the president is taking an unreasonable position to suggest that we ought to treat his request to raise the debt ceiling like some kind of motherhood resolution that everybody says 'aye,' and we don't do anything, when we have the stagnant economy and this massive debt created under his administration,” McConnell told Fox News.

A representative for Speaker John Boehner (R-Ohio) also said Democrats would need to offer concessions to get a debt-ceiling hike through the House.

"The Speaker has said that we should not default on our debt, or even get close to it, but a 'clean' debt limit increase simply won't pass in the House. We hope and expect the White House will work with us on a timely, fiscally responsible solution," Boehner aide Michael Steel said.

But the White House said Monday Obama would not pay "an ideological ransom" in exchange for raising the debt ceiling.

"The American people cannot — and the president will not on their behalf — pay an ideological ransom just so that Congress will do its job and pay the bills that Congress has racked up," White House press secretary Jay Carney said. "It's just irresponsible."